How Can Single Sensory Neurons Predict Behavior?

How Can Single Sensory Neurons Predict Behavior? Pitkow Liu Angelaki DeAngelis Pouget

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How Can Single Sensory Neurons Predict Behavior? 2015 Neuron 10.1016/j.neuron.2015.06.033 Pitkow2015-how-can-single-sensory-neurons-predict-behav Pitkow2015-how-can-single-sensory-neurons-predict-behav.txt, the project's staged copy dc053c111c1ce85b30c8ea7432f4671faa1cfab8 not-redistributable neuroscience

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them why SINGLE SENSORY NEURONS CAN BE SURPRISINGLY PREDICTIVE OF BEHAVIOR IN DISCRIMINATION TASKS Quotation withheld because this record is not cleared for redistribution. which of two accounts is right, given that BOTH SUBOPTIMAL DECODING AND INFORMATION-LIMITING NOISE CORRELATIONS COULD EXPLAIN THESE TWO PUZZLING PHENOMENA - WHICH IS THE CORRECT EXPLANATION? Quotation withheld because this record is not cleared for redistribution. a pair of quantitative predictions that separate the two accounts, and the finding that CHOICE CORRELATIONS CAN BE USED TO ASSESS THE EFFICIENCY OF THE DOWNSTREAM READ-OUT AND DETECT THE PRESENCE OF INFORMATION-LIMITING CORRELATIONS Quotation withheld because this record is not cleared for redistribution. mechanism Quotation withheld because this record is not cleared for redistribution. choice correlations between sensory neurons and perceptual decisions Quotation withheld because this record is not cleared for redistribution. electrophysiology electrophysiology Quotation withheld because this record is not cleared for redistribution. mechanisms Noise correlations aligned with the stimulus-induced change in mean firing (differential correlations) are indistinguishable from real signal, so pooling cannot average them away; population information saturates and single-neuron thresholds stay close to the behavioral threshold, producing large choice correlations. Quotation withheld because this record is not cleared for redistribution. mechanisms A decoder blind to correlations fails to cancel the shared noise fluctuations, so the animal's choice is driven by that irrelevant common noise and every neuron sharing it becomes correlated with the choice. Quotation withheld because this record is not cleared for redistribution. mechanisms An undecoded population inherits information-limiting noise that is partially shared with the decoded population but of larger amplitude, which inflates its choice correlations above the optimal prediction while it contributes nothing to the decision. Quotation withheld because this record is not cleared for redistribution. under optimal decoding THE CHOICE CORRELATIONS TAKE THE REMARKABLY SIMPLE FORM OF A RATIO OF DISCRIMINATION THRESHOLDS - and this prediction HAS NO FREE PARAMETERS Quotation withheld because this record is not cleared for redistribution. the information cannot be created downstream: IF INFORMATION IS NOT AVAILABLE AT THE INPUT, THEN IT CANNOT BE CREATED LATER BY ADDING MORE NEURONS - THOSE EXTRA NEURONS MAY APPEAR TO ADD MORE SIGNAL STRENGTH, BUT THEY ALSO INHERIT NOISE WITH THE SAME STRUCTURE AS THE SIGNAL Quotation withheld because this record is not cleared for redistribution. and that noise cannot be pooled away: THESE INFORMATION-LIMITING CORRELATIONS CANNOT BE AVERAGED AWAY BY APPROPRIATELY POOLING MANY NEURONS, BECAUSE THESE NOISE FLUCTUATIONS ARE INDISTINGUISHABLE FROM CHANGES IN NEURAL ACTIVITY INDUCED BY A REAL SIGNAL Quotation withheld because this record is not cleared for redistribution. ONLY NOISE CORRELATIONS THAT MIMIC THE EFFECT OF THE STIMULUS ON POPULATION ACTIVITY LEAD TO SIGNIFICANT CHOICE CORRELATIONS - called DIFFERENTIAL CORRELATIONS BECAUSE THE CORRELATIONS MIMIC THE RELEVANT SIGNAL WHICH IS THE DIFFERENTIAL (DERIVATIVE) OF THE MEAN RESPONSES Quotation withheld because this record is not cleared for redistribution. Measurement noise leaves open other classes of suboptimal decoder that were not tested what this limits: the decoder conclusion: IT REMAINS POSSIBLE THAT NEURAL PROCESSING IS EVEN BETTER DESCRIBED BY SOME OTHER CLASS OF SUBOPTIMAL DECODERS THAT WE DID NOT CONSIDER Quotation withheld because this record is not cleared for redistribution. The conclusions depend on the specific class of suboptimal (correlation-blind) decoders considered what this limits: the same scope as limitations[0]: THESE RESULTS DEPEND ON THE PARTICULAR CLASS OF SUBOPTIMAL DECODERS WE CONSIDERED ... NAMELY THE CORRELATION-BLIND DECODERS Quotation withheld because this record is not cleared for redistribution. A decoder that removes only the noisiest mode cannot be definitively excluded what this limits: the noisiest-mode argument specifically: WE CANNOT DEFINITIVELY RULE IT OUT Quotation withheld because this record is not cleared for redistribution. The optimality test depends on measuring neural thresholds from signals that are not known to be the ones driving behavior what this limits: the optimality test itself: IDEALLY, WE WOULD LIKE TO COMPUTE NEURAL THRESHOLDS FROM THE SAME NEURAL SIGNALS THAT DRIVE THE BEHAVIOR, BUT WE DON'T KNOW PRECISELY WHAT THOSE SIGNALS ARE Quotation withheld because this record is not cleared for redistribution. the quantity the whole account turns on is not directly measurable - INFORMATION-LIMITING CORRELATIONS ARE DIFFICULT TO ESTIMATE DIRECTLY, REQUIRING LARGE SIMULTANEOUS RECORDINGS WITH MANY TRIALS, and EXTRAPOLATING THE FULL NOISE CORRELATIONS FROM A SPARSE SUBSET OF PAIRWISE CORRELATION MEASUREMENTS IS EXTREMELY DIFFICULT, AND MISTAKES CAN RADICALLY CHANGE THE ESTIMATED INFORMATION CONTENT what this limits: any claim about the information content of a population built from pairwise correlation measurements Quotation withheld because this record is not cleared for redistribution. the conclusion is relative to one family of alternatives - THESE RESULTS DEPEND ON THE PARTICULAR CLASS OF SUBOPTIMAL DECODERS WE CONSIDERED IN THE EXTENSIVE INFORMATION CASE, NAMELY THE CORRELATION-BLIND DECODERS, which is QUITE GENERAL, ALTHOUGH NOT ALL-ENCOMPASSING what this limits: the suboptimality conclusion, which is relative to one family: THESE RESULTS DEPEND ON THE PARTICULAR CLASS OF SUBOPTIMAL DECODERS WE CONSIDERED ... NAMELY THE CORRELATION-BLIND DECODERS Quotation withheld because this record is not cleared for redistribution. DUE TO MEASUREMENT NOISE IN THE DATA, IT REMAINS POSSIBLE THAT NEURAL PROCESSING IS EVEN BETTER DESCRIBED BY SOME OTHER CLASS OF SUBOPTIMAL DECODERS THAT WE DID NOT CONSIDER duplicate of: limitations[0] · what this limits: the same scope as limitations[0] - DUE TO MEASUREMENT NOISE IN THE DATA, IT REMAINS POSSIBLE THAT NEURAL PROCESSING IS EVEN BETTER DESCRIBED BY SOME OTHER class of decoder Quotation withheld because this record is not cleared for redistribution. and the authors say the model cannot be forced to fail - WE CAN ALWAYS CONCOCT SOME COMBINATION OF CORRELATIONS AND SUBOPTIMAL DECODERS THAT WOULD BE CONSISTENT WITH FINE DETAILS OF OUR MEASUREMENTS, rejected on the ground that it WOULD REQUIRE UNPALATABLE FINE-TUNING OF THE MODEL what this limits: treating the conclusion as an exclusion rather than as a parsimony judgment Quotation withheld because this record is not cleared for redistribution. the two hypotheses are only separable if the sample is diverse enough - THE PREDICTIONS FOR OPTIMAL DECODING COULD BE SATISFIED EVEN FOR A POPULATION OF NEURONS DECODED SUBOPTIMALLY, LEADING US TO MISCHARACTERIZE A SUBOPTIMAL SYSTEM AS OPTIMAL, and THAT NEARLY HAPPENS FOR A HOMOGENEOUS POPULATION what this limits: applying the test in a preparation whose tuning curves are not heterogeneous Quotation withheld because this record is not cleared for redistribution. one monkey's data did not decide anything - CHOICE CORRELATIONS FOR MSTd IN THE OTHER MONKEY WERE INCONCLUSIVE what this limits: the MSTd evidence specifically: CHOICE CORRELATIONS FOR MSTd IN THE OTHER MONKEY WERE INCONCLUSIVE Quotation withheld because this record is not cleared for redistribution. a result of this paper is that an elegant earlier method may not work - SUCH A FULL RECONSTRUCTION MAY NOT BE FEASIBLE IN THE PRESENCE OF INFORMATION-LIMITING CORRELATIONS, and IT MAY NOT BE POSSIBLE TO USE CHOICE PROBABILITIES TO COMPUTE DECODING WEIGHTS FROM EXPERIMENTAL DATA what this limits: the earlier weight-reconstruction method, which this result bears on: DESPITE THE ELEGANCE OF THIS RESULT, ONE CONSEQUENCE OF OUR FI[ndings is that] SUCH A FULL RECONSTRUCTION MAY NOT BE [possible] Quotation withheld because this record is not cleared for redistribution. THE DATA PROCESSING INEQUALITY, used to rule out a model of cortical coding outright - THE EXTENSIVE INFORMATION MODEL ATTRIBUTES MORE INFORMATION TO THE CORTEX THAN TO THE SENSORS, AND THIS IS PROHIBITED Quotation withheld because this record is not cleared for redistribution. the Akaike Information Criterion, used to choose between five predictors of the same measurements - and OUR DATA WAS STRONG ENOUGH TO SIGNIFICANTLY DIFFERENTIATE BETWEEN THE MODELS Quotation withheld because this record is not cleared for redistribution. the whole discrimination procedure run first on simulated populations whose decoder was known eliminates: the method not being able to tell the two hypotheses apart at all - IN ALL FOUR MODEL SYSTEMS, THIS METHOD WAS ABLE TO RECOVER THE TRUE VALUES OF BOTH COEFFICIENTS WITHIN THE SIMULATED EXPERIMENTAL UNCERTAINTY · outcome: held Quotation withheld because this record is not cleared for redistribution. three further optimality signatures checked, each of which could have failed eliminates: optimality being read off one fit - uninformative neurons had choice correlations NO MORE THAN EXPECTED BY CHANCE, NO NEURONS HAVE A THRESHOLD LOWER THAN THE ANIMAL'S BEHAVIORAL THRESHOLD, and negative choice correlations excluded zero for ONLY 4/339 RECORDED CELLS · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. a neuron-antineuron correction applied to the neural thresholds that an earlier study omitted eliminates: NO NEURONS HAVE A THRESHOLD LOWER THAN THE ANIMAL'S BEHAVIORAL THRESHOLD, AS LONG AS NEURAL THRESHOLDS ARE PROPERLY CORRECTED FOR USE OF A NEURON-ANTINEURON PAIR - A CORRECTION THAT WAS NOT APPLIED IN ( COHEN AND NEWSOME 2009 ) · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. model quality scored by AIC against a null model and three alternatives eliminates: a better fit bought with free parameters - and OUR DATA WAS STRONG ENOUGH TO SIGNIFICANTLY DIFFERENTIATE BETWEEN THE MODELS · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. choice probability choice probability Quotation withheld because this record is not cleared for redistribution. threshold threshold Quotation withheld because this record is not cleared for redistribution. efficiency efficiency Quotation withheld because this record is not cleared for redistribution. noise fluctuations → real signal PROVED INDISTINGUISHABLE - the FORMAL form / Not 'we could not tell them apart' but 'they cannot be told apart'. AND IT SURVIVES THE OBVIOUS REMEDY: 'These information-limiting correlations cannot be averaged away by appropriately pooling many neurons, because these noise fluctuations are indistinguishable from changes in neural activity induced by a real signal'. The indistinguishability is the REASON pooling fails, so it is load-bearing for the paper's conclusion rather than a caveat on it. Quotation withheld because this record is not cleared for redistribution. THE LARGEST CORRELATION WITH CHOICE SITS IN THE AREA THAT DOES NOT MATTER: REVERSIBLE CHEMICAL INACTIVATION OF VIP DOES NOT IMPAIR HEADING DISCRIMINATION, DESPITE THE FACT THAT VIP NEURONS EXHIBIT LARGE CHOICE CORRELATIONS - and the same holds in another area, ANOTHER RECENT STUDY OF THE PARIETAL CORTEX (AREA LIP) ALSO REPORTS HIGH CHOICE CORRELATIONS, YET INACTIVATING THIS REGION AGAIN HAS NO DISCERNIBLE EFFECT ON VISUAL MOTION DISCRIMINATION Quotation withheld because this record is not cleared for redistribution. and the paper's own summary says the same in its own voice: VIP EXHIBITS HIGH CHOICE PROBABILITIES AND ROBUST NOISE CORRELATIONS MUCH LIKE VN/CN, YET OUR ANALYSIS SUGGESTS THAT VIP IS DECODED SUBOPTIMALLY, IF AT ALL Quotation withheld because this record is not cleared for redistribution. THE FIELD'S STANDARD MEASURE OF A NEURON'S INVOLVEMENT IS THEREFORE NOT A MEASURE OF INVOLVEMENT: the brain LOSES VERY LITTLE INFORMATION BY IGNORING VIP, and the choice correlations there are the largest of the three areas Quotation withheld because this record is not cleared for redistribution. THE PAPER STATES THE RULE THIS PROJECT CALLS WITHIN-RUN COMPARISONS ONLY: IF DIFFERENT BRAIN REGIONS SEEM TO HAVE DIFFERENT CHOICE CORRELATIONS, ONE MUST TAKE CARE TO ACCOUNT FOR DIFFERENCES IN PSYCHOPHYSICAL SENSITIVITY BETWEEN ANIMALS BEFORE CONCLUDING THAT THE DIFFERENCE BETWEEN BRAIN AREAS IS MEANINGFUL - THE SUREST DIAGNOSTIC WOULD BE TO MEASURE CHOICE CORRELATIONS FROM MULTIPLE AREAS WITHIN A SINGLE ANIMAL. The measure has the animal's own threshold in its denominator Quotation withheld because this record is not cleared for redistribution. THE SAME NUMBER MEANS OPTIMAL OR SUBOPTIMAL DEPENDING ON A CONSTANT: SUCH A PATTERN OF CHOICE CORRELATIONS INDICATES OPTIMAL DECODING IF AND ONLY IF THE PROPORTIONALITY CONSTANT EQUALS THE THRESHOLD OF POPULATION ACTIVITY - ALL OTHER VALUES OF THE PROPORTIONALITY CONSTANT REFLECT SUBOPTIMAL DECODING. The pattern alone is not the finding Quotation withheld because this record is not cleared for redistribution. and a scale above one is diagnostic of the opposite of what it looks like: CHOICE CORRELATIONS PROPORTIONAL BUT NOT EQUAL TO THE OPTIMAL PREDICTION OCCUR ONLY WITH SOME DEGREE OF SUBOPTIMAL DECODING - WHENEVER THE CHOICE CORRELATIONS HAVE β ≠1, THE EFFICIENCY IS LESS THAN 1 Quotation withheld because this record is not cleared for redistribution. THE COUNTER-INTUITIVE CASE, WORKED OUT: choice correlations LARGER than the optimal prediction arise WHEN BEHAVIOR IS DRIVEN BY ANOTHER, MORE INFORMATIVE, SOURCE OF SENSORY SIGNALS BESIDE THE NEURAL POPULATION UNDER STUDY - a neuron can be perfectly correlated with a choice it plays no part in Quotation withheld because this record is not cleared for redistribution. TWO HYPOTHESES ARE ONLY DISTINGUISHABLE IF THE SAMPLE IS DIVERSE: THE PREDICTIONS FOR OPTIMAL DECODING COULD BE SATISFIED EVEN FOR A POPULATION OF NEURONS DECODED SUBOPTIMALLY, LEADING US TO MISCHARACTERIZE A SUBOPTIMAL SYSTEM AS OPTIMAL, and THAT NEARLY HAPPENS FOR A HOMOGENEOUS POPULATION. The discriminating power of the test is a property of the sample, not of the theory Quotation withheld because this record is not cleared for redistribution. AND AN EARLIER RESULT HOLDS ONLY UNDER ITS OWN IDEALISATION: WEAK POSITIVE NOISE CORRELATIONS DO NOT ALWAYS PRODUCE LARGE CHOICE CORRELATIONS - THIS IS ONLY TRUE FOR THE MODEL THEY CONSIDER WITH HOMOGENEOUS NEURONS AND HOMOGENEOUS NOISE CORRELATIONS Quotation withheld because this record is not cleared for redistribution. A MODEL RULED OUT BY A MATHEMATICAL LAW RATHER THAN BY DATA: SINCE CORTICAL POPULATIONS ARE MUCH LARGER THAN THE SENSORY POPULATION BUT NOT MUCH NOISIER, THE EXTENSIVE INFORMATION MODEL ATTRIBUTES MORE INFORMATION TO THE CORTEX THAN TO THE SENSORS - AND THIS IS PROHIBITED BY THE DATA PROCESSING INEQUALITY Quotation withheld because this record is not cleared for redistribution. and one hypothesis killed by an order-of-magnitude argument: THE CHOICE CORRELATIONS WOULD THEN BE CORRESPONDINGLY TINY, AND MOST LIKELY NOT SIGNIFICANTLY DIFFERENT FROM ZERO GIVEN TYPICAL MEASUREMENT UNCERTAINTY - THIS ARGUMENT RULES OUT MODELS IN WHICH THE BRAIN HAS EXTENSIVE INFORMATION AND DECODES IT OPTIMALLY Quotation withheld because this record is not cleared for redistribution. TWO CONVENTIONAL EXPECTATIONS REVERSED. First: CHOICE CORRELATION SHOULD BE SMALLER FOR LARGER POPULATIONS SINCE INFORMATION IS DISTRIBUTED ACROSS MORE NEURONS - HOWEVER, IF THE CODE IS REDUNDANT AND DECODED NEAR-OPTIMALLY, THEN THE CHOICE CORRELATIONS DO NOT VARY WITH POPULATION SIZE Quotation withheld because this record is not cleared for redistribution. Second, and it can invert: CHOICE CORRELATIONS SHOULD BE GREATER WHEN NOISE CORRELATIONS ARE LARGER - THIS IS TRUE ONLY FOR A SPECIFIC PATTERN OF CORRELATIONS, OR FOR CERTAIN TYPES OF DECODERS, and CHOICE CORRELATIONS COULD POTENTIALLY RISE EVEN WHILE THE TOTAL NOISE CORRELATION FALLS Quotation withheld because this record is not cleared for redistribution. OPTIMALITY IS CHEAP AND THE PAPER SAYS SO: ACHIEVING NEAR-OPTIMAL PERFORMANCE MAY NOT BE SUCH AN IMPRESSIVE FEAT, AS OUR RESULTS IMPLY THAT THE INFORMATION ENCODED IN NEURAL POPULATIONS IS HIGHLY REDUNDANT AND THEREFORE ROBUST TO SUBOPTIMAL DECODING - OPTIMALITY MEASURES THE QUALITY OF DECODING, RATHER THAN THE PARTICULAR NETWORK STRUCTURE USED TO DECODE Quotation withheld because this record is not cleared for redistribution. so the label does not identify the mechanism: A BROAD RANGE OF DECODERS MAY ALL PRODUCE SIMILAR NEAR-OPTIMAL PERFORMANCE, and THE TRUE DECODING WEIGHTS COULD RESEMBLE THOSE OF A CORRELATION-BLIND DECODER, OR MANY OTHER DECODERS, AND YET BE NEAR-OPTIMAL Quotation withheld because this record is not cleared for redistribution. THE QUANTITY THE ARGUMENT TURNS ON CANNOT BE MEASURED DIRECTLY: INFORMATION-LIMITING CORRELATIONS ARE DIFFICULT TO ESTIMATE DIRECTLY, THE INFORMATION-LIMITING COMPONENT CAN BE VERY SMALL YET HAVE ENORMOUS EFFECTS ON POPULATION INFORMATION, and MISTAKES CAN RADICALLY CHANGE THE ESTIMATED INFORMATION CONTENT OF A NEURAL POPULATION - so it is inferred from an INDIRECT CONSEQUENCE observable with single neurons Quotation withheld because this record is not cleared for redistribution. and it is invisible by construction: INFORMATION-LIMITING NOISE CORRELATIONS MAY HIDE ESSENTIALLY UNNOTICED AMONGST OTHER NOISE CORRELATIONS WITH HIGHER VARIANCE THAT ARISE DOWNSTREAM, because THESE NOISE FLUCTUATIONS ARE INDISTINGUISHABLE FROM CHANGES IN NEURAL ACTIVITY INDUCED BY A REAL SIGNAL Quotation withheld because this record is not cleared for redistribution. A PREDICTION WITH NO FREE PARAMETERS, AND THE AUTHORS SAY SO: THE RATIO OF PSYCHOPHYSICAL TO NEURAL THRESHOLDS DID A REASONABLE JOB OF PREDICTING THE MEASURED CHOICE CORRELATIONS - WE EMPHASIZE THAT THIS PREDICTION HAS NO FREE PARAMETERS Quotation withheld because this record is not cleared for redistribution. AN ADMISSION THAT THE MODEL CANNOT BE FORCED TO FAIL: WE CAN ALWAYS CONCOCT SOME COMBINATION OF CORRELATIONS AND SUBOPTIMAL DECODERS THAT WOULD BE CONSISTENT WITH FINE DETAILS OF OUR MEASUREMENTS - HOWEVER, THIS WOULD REQUIRE UNPALATABLE FINE-TUNING OF THE MODEL. The conclusion is a parsimony judgment and is labelled as one Quotation withheld because this record is not cleared for redistribution. THE INFORMATION CANNOT BE MANUFACTURED DOWNSTREAM: IF INFORMATION IS NOT AVAILABLE AT THE INPUT, THEN IT CANNOT BE CREATED LATER BY ADDING MORE NEURONS - THOSE EXTRA NEURONS MAY APPEAR TO ADD MORE SIGNAL STRENGTH, BUT THEY ALSO INHERIT NOISE WITH THE SAME STRUCTURE AS THE SIGNAL Quotation withheld because this record is not cleared for redistribution. and the empirical answer: THE RESULTANT REGRESSION COEFFICIENTS ON THE SUBOPTIMAL PREDICTORS WERE NEAR ZERO, WHEREAS THOSE ON OPTIMAL PREDICTORS WERE CLOSE TO ONE - THE INFORMATION AVAILABLE IN THE VESTIBULAR AND CEREBELLAR NUCLEI IS USED NEAR-OPTIMALLY, AND BEHAVIORAL PERFORMANCE IS LIMITED PRIMARILY BY CORRELATED NOISE, NOT SUBOPTIMAL DECODING Quotation withheld because this record is not cleared for redistribution. claim_type: mechanism a second reading reaching the same value. Recorded: mechanism — note: a second reading reaching the same value from a different sentence. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. method: derive the choice-correlation pattern each hypothesis implies, verify on simulated populations that the two can be told apart, then fit both predictors to recorded neurons by linear regression and compare models by AIC a second reading DIFFERING from the recorded value. Recorded: electrophysiology — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. phenomenon: a correlation between a single neuron's firing and the animal's choice, which is large and common where the theory of the day says it should be immeasurably small a second reading DIFFERING from the recorded value. Recorded: choice correlations between sensory neurons and perceptual decisions — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. extends → Haefner, Gerwinn et al. 2013 Quotation withheld because this record is not cleared for redistribution. builds-on → Moreno-Bote, Beck et al. 2014 (differential correlations) Quotation withheld because this record is not cleared for redistribution. contradicts → Shamir and Sompolinsky 2006; Ecker, Berens et al. 2011 (extensive-information models of population codes) Quotation withheld because this record is not cleared for redistribution. qualifies → Zohary, Shadlen et al. 1994, that weakly correlated noise explains covariation of single neurons with decisions differs in: the homogeneity of the model - WEAK POSITIVE NOISE CORRELATIONS DO NOT ALWAYS PRODUCE LARGE CHOICE CORRELATIONS - THIS IS ONLY TRUE FOR THE MODEL THEY CONSIDER WITH HOMOGENEOUS NEURONS AND HOMOGENEOUS NOISE CORRELATIONS Quotation withheld because this record is not cleared for redistribution. contradicts → models in which cortical populations carry extensive information that is decoded optimally differs in: what the choice correlations would then have to be - CORRESPONDINGLY TINY, AND MOST LIKELY NOT SIGNIFICANTLY DIFFERENT FROM ZERO GIVEN TYPICAL MEASUREMENT UNCERTAINTY Quotation withheld because this record is not cleared for redistribution. critiques → Haefner, Gerwinn et al. 2013's reconstruction of decoding weights from choice probabilities differs in: whether information-limiting correlations are present - MANY DIFFERENT DECODING WEIGHT PROFILES CAN EXTRACT NEARLY ALL OF THE AVAILABLE INFORMATION Quotation withheld because this record is not cleared for redistribution. extends → Haefner, Gerwinn et al. 2013's analysis of choice probability, extended to information-limiting correlations and suboptimal decoding Quotation withheld because this record is not cleared for redistribution. contradicts → the expectation that choice correlations shrink as the decoded population grows differs in: whether the code is redundant - IF THE CODE IS REDUNDANT AND DECODED NEAR-OPTIMALLY, THEN THE CHOICE CORRELATIONS DO NOT VARY WITH POPULATION SIZE Quotation withheld because this record is not cleared for redistribution. reconciles → large choice correlations in VIP against the null effect of inactivating it status: the paper's own words: preliminary results · differs in: whether the area is decoded - VIP IS NOT DECODED FOR HEADING DISCRIMINATION BUT NONETHELESS CONTAINS INFORMATION THAT IS CORRELATED WITH ANOTHER AREA THAT IS DECODED NEAR-OPTIMALLY Quotation withheld because this record is not cleared for redistribution. VIP —contrasted-with→ MSTd VIP MSTd differs in: THE AXIS IS WHETHER THE AVAILABLE INFORMATION IS ACTUALLY USED. 'Quotation withheld.' The areas are not distinguished by what they encode but by what the animal does with it - and 'for this task' bounds it, so the same area could be read efficiently elsewhere. · strength of the relation: 1 · note: Quotation withheld Quotation withheld because this record is not cleared for redistribution. choice correlation —operationalised-as→ threshold choice correlation threshold strength of the relation: 1 · note: FOR OPTIMAL COMPUTATION, THE CHOICE CORRELATIONS TAKE THE REMARKABLY SIMPLE FORM OF A RATIO OF DISCRIMINATION THRESHOLDS Quotation withheld because this record is not cleared for redistribution. optimal decoding —contrasted-with→ suboptimal decoding optimal decoding suboptimal decoding strength of the relation: 1 · note: BOTH SUBOPTIMAL DECODING AND INFORMATION-LIMITING NOISE CORRELATIONS COULD EXPLAIN THESE TWO PUZZLING PHENOMENA. WHICH IS THE CORRECT EXPLANATION? Quotation withheld because this record is not cleared for redistribution. decoder —operationalised-as→ correlation-blind decoder correlation-blind strength of the relation: 0.8 · note: THE PARTICULAR CLASS OF SUBOPTIMAL DECODERS WE CONSIDERED... NAMELY THE CORRELATION-BLIND DECODERS, which is QUITE GENERAL, ALTHOUGH NOT ALL-ENCOMPASSING Audit 2026-09-28: DOUBTFUL - read against its span and kept, but correlation-blind decoders are the class considered; operationalised-as is loose. Quotation withheld because this record is not cleared for redistribution. information-limiting —part-of→ noise correlations information-limiting noise correlations strength of the relation: 0.3 — the record marks this weak · note: INFORMATION-LIMITING NOISE CORRELATIONS MAY HIDE ESSENTIALLY UNNOTICED AMONGST OTHER NOISE CORRELATIONS WITH HIGHER VARIANCE THAT ARISE DOWNSTREAM Quotation withheld because this record is not cleared for redistribution. differential correlations —causes→ choice correlation differential correlations choice correlation strength of the relation: 1 · note: THE ONLY NOISE CORRELATIONS THAT LEAD TO SIGNIFICANT CHOICE CORRELATIONS ARE THOSE THAT MIMIC THE EFFECT OF THE STIMULUS ON POPULATION ACTIVITY Quotation withheld because this record is not cleared for redistribution. noise correlations —contrasted-with→ choice correlation noise correlations choice correlation differs in: THE AXIS IS THE DECODING REGIME. 'choice correlations should be greater when noise correlations are larger ... This is true only for A specific pattern of correlations, or for certain types of decoders. For SUBOPTIMAL DECODING of highly informative populations, choice correlations DO increase with the overall scale of correlated noise. However, our results instead favor near-optimal decoding, for which most correlations play little role.' The expected relationship is not denied - it is confined to a decoding assumption, and the assumption is not a property of the data. · strength of the relation: 0.4 — the record marks this weak · note: CHOICE CORRELATIONS COULD POTENTIALLY RISE EVEN WHILE THE TOTAL NOISE CORRELATION FALLS Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but choice correlations rise with noise correlations only for certain patterns or decoders; contrasted-with is loose. Quotation withheld because this record is not cleared for redistribution. population —contrasted-with→ choice correlation population choice correlation strength of the relation: 0.3 — the record marks this weak · note: IF THE CODE IS REDUNDANT AND DECODED NEAR-OPTIMALLY, THEN THE CHOICE CORRELATIONS DO NOT VARY WITH POPULATION SIZE Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span discusses how choice correlation scales with population size; contrasted-with is loose. Quotation withheld because this record is not cleared for redistribution. choice probability —same-as→ choice correlation choice probability choice correlation strength of the relation: 0.8 · note: THIS QUANTITY HAS A SIMPLE, NEARLY AFFINE RELATIONSHIP TO CHOICE PROBABILITY... BUT IT IS CONCEPTUAL SIMPLER AND MATHEMATICALLY MORE CONVENIENT Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but choice correlation has 'a simple, NEARLY AFFINE relationship to' choice probability; same-as is loose. Quotation withheld because this record is not cleared for redistribution. regression regression Quotation withheld because this record is not cleared for redistribution. Akaike Information Criterion Akaike Information Criterion Quotation withheld because this record is not cleared for redistribution. bootstrap bootstrap Quotation withheld because this record is not cleared for redistribution. permutation test permutation test Quotation withheld because this record is not cleared for redistribution. t-test t-test Quotation withheld because this record is not cleared for redistribution. correlation correlation Quotation withheld because this record is not cleared for redistribution. ROC analysis ROC analysis Quotation withheld because this record is not cleared for redistribution. maximum likelihood estimation maximum likelihood estimation Quotation withheld because this record is not cleared for redistribution. confidence interval confidence interval Quotation withheld because this record is not cleared for redistribution. standard deviation standard deviation Quotation withheld because this record is not cleared for redistribution. Akaike Information Criterion Akaike Information Criterion Quotation withheld because this record is not cleared for redistribution. linear regression linear regression Quotation withheld because this record is not cleared for redistribution. t -test t -test Quotation withheld because this record is not cleared for redistribution. More informative neurons - those with lower discrimination thresholds - correlate more strongly with the animal's choice. Quotation withheld because this record is not cleared for redistribution. The two competing explanations are separable in the data because optimal decoding predicts choice correlations that scale with each neuron's threshold and ignore its preferred stimulus, while correlation-blind suboptimal decoding predicts the reverse. Quotation withheld because this record is not cleared for redistribution. Quotation withheld Quotation withheld because this record is not cleared for redistribution. Quotation withheld Quotation withheld because this record is not cleared for redistribution. MSTd and VN/CN carry redundant heading codes read out near-optimally, whereas the data suggest VIP's information is not used efficiently for this task. Quotation withheld because this record is not cleared for redistribution. However the population is decoded, information-limiting noise keeps the variance of any unbiased linear estimator from falling below ε. Quotation withheld because this record is not cleared for redistribution. Because information-limited population codes are highly redundant, a wide range of suboptimal decoders performs almost as well as the optimal one. Quotation withheld because this record is not cleared for redistribution. Confidence intervals excluded zero from below for only 4 of 339 recorded cells, a proportion that is not significant. Quotation withheld because this record is not cleared for redistribution. No recorded neuron had a discrimination threshold better than the animal's behavioral threshold once thresholds were corrected for the neuron-antineuron pairing, as optimal computation requires. Quotation withheld because this record is not cleared for redistribution. Contrary to the common expectation that choice correlations shrink as the pool of neurons grows, they are independent of population size when the code is redundant and read out near-optimally. Quotation withheld because this record is not cleared for redistribution. REVERSIBLE CHEMICAL INACTIVATION OF VIP DOES NOT IMPAIR HEADING DISCRIMINATION, DESPITE THE FACT THAT VIP NEURONS EXHIBIT LARGE CHOICE CORRELATIONS Quotation withheld because this record is not cleared for redistribution. ANOTHER RECENT STUDY OF THE PARIETAL CORTEX (AREA LIP) ALSO REPORTS HIGH CHOICE CORRELATIONS, YET INACTIVATING THIS REGION AGAIN HAS NO DISCERNIBLE EFFECT ON VISUAL MOTION DISCRIMINATION Quotation withheld because this record is not cleared for redistribution. THE RESULTANT REGRESSION COEFFICIENTS ON THE SUBOPTIMAL PREDICTORS WERE NEAR ZERO, WHEREAS THOSE ON OPTIMAL PREDICTORS WERE CLOSE TO ONE Quotation withheld because this record is not cleared for redistribution. THE PREDICTION OF SUBOPTIMAL DECODING WAS POORLY MATCHED TO DATA ACROSS ALL AREAS Quotation withheld because this record is not cleared for redistribution. NO NEURONS HAVE A THRESHOLD LOWER THAN THE ANIMAL'S BEHAVIORAL THRESHOLD, AS LONG AS NEURAL THRESHOLDS ARE PROPERLY CORRECTED FOR USE OF A NEURON-ANTINEURON PAIR Quotation withheld because this record is not cleared for redistribution. the negative choice correlations' 95% CONFIDENCE INTERVALS EXCLUDE ZERO FROM BELOW FOR ONLY 4/339 RECORDED CELLS, A PROPORTION WHICH IS NOT SIGNIFICANT Quotation withheld because this record is not cleared for redistribution. CHOICE CORRELATIONS PROPORTIONAL BUT NOT EQUAL TO THE OPTIMAL PREDICTION OCCUR ONLY WITH SOME DEGREE OF SUBOPTIMAL DECODING Quotation withheld because this record is not cleared for redistribution. IF THE CODE IS REDUNDANT AND DECODED NEAR-OPTIMALLY, THEN THE CHOICE CORRELATIONS DO NOT VARY WITH POPULATION SIZE Quotation withheld because this record is not cleared for redistribution. CHOICE CORRELATIONS COULD POTENTIALLY RISE EVEN WHILE THE TOTAL NOISE CORRELATION FALLS Quotation withheld because this record is not cleared for redistribution. WEAK POSITIVE NOISE CORRELATIONS DO NOT ALWAYS PRODUCE LARGE CHOICE CORRELATIONS - THIS IS ONLY TRUE FOR THE MODEL THEY CONSIDER WITH HOMOGENEOUS NEURONS AND HOMOGENEOUS NOISE CORRELATIONS Quotation withheld because this record is not cleared for redistribution. choice correlation choice correlation Quotation withheld because this record is not cleared for redistribution. choice probability choice probability Quotation withheld because this record is not cleared for redistribution. differential correlations differential correlations Quotation withheld because this record is not cleared for redistribution. discrimination threshold discrimination threshold Quotation withheld because this record is not cleared for redistribution. factorial decoder factorial decoder Quotation withheld because this record is not cleared for redistribution. correlation-blind decoder correlation-blind decoder Quotation withheld because this record is not cleared for redistribution. psychophysical threshold psychophysical threshold Quotation withheld because this record is not cleared for redistribution. decoder efficiency decoder efficiency Quotation withheld because this record is not cleared for redistribution. THE PROBABILITY THAT A NEURAL RESPONSE ASSOCIATED WITH ONE BEHAVIORAL CHOICE IS GREATER THAN A NEURAL RESPONSE ASSOCIATED WITH THE OTHER POSSIBLE CHOICE choice probability Quotation withheld because this record is not cleared for redistribution. THE SIGNAL CHANGE REQUIRED TO EXCEED ONE STANDARD DEVIATION OF NOISE threshold Quotation withheld because this record is not cleared for redistribution. noise correlations that MIMIC THE RELEVANT SIGNAL WHICH IS THE DIFFERENTIAL (DERIVATIVE) OF THE MEAN RESPONSES differential correlations Quotation withheld because this record is not cleared for redistribution. heading direction heading direction Quotation withheld because this record is not cleared for redistribution. decoding strategy decoding strategy Quotation withheld because this record is not cleared for redistribution. choice correlations, neural thresholds and behavioral thresholds choice correlations, neural thresholds and behavioral thresholds Quotation withheld because this record is not cleared for redistribution. fixation fixation Quotation withheld because this record is not cleared for redistribution. choice correlation choice correlation Quotation withheld because this record is not cleared for redistribution. threshold threshold Quotation withheld because this record is not cleared for redistribution. r =.26 — correlation between the optimal and correlation-blind predicted choice correlations in simulation, showing the two predictions are nearly independent Quotation withheld because this record is not cleared for redistribution. 4/339 — recorded cells whose choice correlation was significantly negative, a proportion no greater than chance Quotation withheld because this record is not cleared for redistribution. p =.10 — test of whether uninformative (very high threshold) neurons had non-zero choice correlations more often than chance Quotation withheld because this record is not cleared for redistribution. 77% (75/97) — share of VN/CN neurons held long enough for at least 20 repetitions per stimulus (with 95% in MSTd and 69% in VIP) Quotation withheld because this record is not cleared for redistribution. 30-fold — how much better than a single neuron behavior should be for 1000 optimally decoded neurons with extensive information — far better than observed Quotation withheld because this record is not cleared for redistribution. 80% — efficiency of a decoder that reads out only the more informative of two correlated populations in the illustrated covariance case Quotation withheld because this record is not cleared for redistribution. α =0.9 — simulation setting where 90% of the stimulus-estimate variance came from information-limiting correlations Quotation withheld because this record is not cleared for redistribution. 0.1 to 0.5 — typical empirical range of c0, the proportionality between signal and noise correlations Quotation withheld because this record is not cleared for redistribution. 500 — number of neurons in each simulated population Quotation withheld because this record is not cleared for redistribution. Eight — rhesus monkeys implanted and recorded from Quotation withheld because this record is not cleared for redistribution. 400 msec — spike-count window around peak movement velocity assumed to carry the decision-relevant signal Quotation withheld because this record is not cleared for redistribution. (50) ... (30 repetitions) — neurons and trials per stimulus used in the finite-data simulation, matched to the real experiments Quotation withheld because this record is not cleared for redistribution. 4/339 — recorded cells whose negative choice correlation excluded zero - NOT SIGNIFICANT Quotation withheld because this record is not cleared for redistribution. close to one — the regression coefficient on the optimal predictor in VN/CN, with the suboptimal coefficient near zero Quotation withheld because this record is not cleared for redistribution.

The full text of this article is not redistributable, so it is not included here. The evidence sentences are withheld with it; the tag layer and its grounding status remain. The article itself is at https://doi.org/10.1016/j.neuron.2015.06.033.